At VLF and LF, transmitted radio signals consist of many vertically polarized earth-ionosphere waveguide modes which, in general, possess different attenuation rates and different phase velocities. For each different frequency, a signal is represented by the phasor sum of the modes. An incremental phase velocity V.sub.i (D) which V.sub.1 varies directly as a function of distance D is defined as follows: ##EQU1##
In equation (1), .DELTA.D is defined as the incremental change in distance, and .DELTA.t is the incremental change in phase (in seconds, for example) which occurs over the distance increment at a mean distance D from the transmitter.
Total phase change over a great-circle path of distance D can be expressed by the following equation wherein t is expressed in microseconds: ##EQU2## where K is equal to the total number of incremental values in the distance D.
The summation term in equation (2) provides an average phase velocity V for any great-circle path whose distance is equal to D: ##EQU3## where t is again expressed in microseconds.
Experimental work by the inventor has demonstrated that incremental phase velocity V.sub.i (D,t) and average phase velocity change, V(D,t.sub.1)-V(D,t.sub.2) are measurable quantities at VLF and that they can be accurately calculated when certain ionospheric models are assumed. Likewise, it was determined that vertical whip antennas are more effective for HF direction finding applications than loop antennas since vertical whips respond to the vertical field only, whereas loop antennas respond to abnormal field components which cause direction finding errors.